A328924 Triangle T(n,k) read by rows: connected topologies of the effective potential in Goldstone diagrams with n interactions and k external potentials.

1, 0, 1, 2, 0, 1, 12, 12, 6, 2, 300, 336, 168, 48, 6, 13680, 15120, 7560, 2160, 360, 24, 920400, 1000800, 498960, 146880, 27000, 2880, 120, 85004640, 91314720, 45516240, 13698720, 2691360, 342720, 25200, 720, 10314511200, 10981474560, 5476625280, 1675699200, 344433600, 48545280, 4515840, 241920, 5040

Offset: 0

Author

R. J. Mathar, Oct 31 2019

Keywords

• nonn
• tabl

Examples

			         1;
         0          1;
         2          0          1;
        12         12          6          2;
       300        336        168         48          6;
     13680      15120       7560       2160        360         24;
    920400    1000800     498960     146880      27000       2880        120;
  85004640   91314720   45516240   13698720    2691360     342720      25200        720;
		

Links

• P. J. Rossky, M. Karplus, The enumeration of Goldstone diagrams in many-body perturbation theory, J. Chem. Phys. 64 (1976) 1569, Teff(n,k)

Crossrefs

Cf. A328921-A328923.

Formula

T(n,k) = sum_{t=k..n} (-1)^(k+t) *2^(t-k) *binomial(t,k) *A328923(n,t).